Accuracy question

*To*: mathgroup at smc.vnet.net*Subject*: [mg14030] Accuracy question*From*: "Ersek, Ted R" <ErsekTR at navair.navy.mil>*Date*: Wed, 16 Sep 1998 14:12:09 -0400*Sender*: owner-wri-mathgroup at wolfram.com

In the lines below SetPrecision[Round,False] makes it so Precision and accuracy return the actual floating point numbers that are used internally. $NumberMarks=True, makes it so (among other things) InputForm[num] returns all digits used internally, and the precision marks at the end of inexact numbers. In[1]:= SetPrecision[Round,False]; $NumberMarks=True; x=12345.67; Out[2] shows exactly how Precision[x] is represented internally. Out[3] shows that Precision[x] is the number closest to Log[10, 2^53]. In[2]:= Precision[x]//InputForm Out[2]= 15.9545897701910028` In[3]:= N[N[Log[10,2^53],17]]//InputForm Out[3]= 15.9545897701910028` The next line shows exactly how Accuracy[x] is represented internally. Where does this number come from? Since accuracy is the number of digits to the right of the decimal I expect to get roughly 11.9. But why ( 11.8630751061039617` )? In[4]:= Accuracy[x]//InputForm Out[4]= 11.8630751061039617` ______________________________ Cheers, Ted Ersek